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Gamma, Beta, Erf > Gamma[z] > Introduction to the Gamma Function

Connections within the group of gamma functions and with other function groups

The gamma function is the main example of a group of functions collectively referred to as gamma functions. For example, it can be written in terms of the incomplete gamma function:

All four incomplete gamma functions , , , and can be represented as cases of the hypergeometric function . Further, the gamma function Γ(z) is the special degenerate case of the hypergeometric function .

The gamma function and two factorial functions are connected by the formulas: